Subgroups — D₈×#10621872 #25068014

Order 11008.

794 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₈×D₄₃	C₂	1	1	yes	maximal, characteristic
2	D₄×#10621872	C₂	1	2	yes	maximal, complemented
3	#19133481	C₂	1	1	yes	maximal, characteristic, complemented
4	#19133479	C₂	1	1	yes	maximal, characteristic, complemented
5	#19133424	C₂	1	2	yes	maximal, complemented
6	#19133421	C₂	1	2	yes	maximal, complemented
7	D₈×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	#19133352	C₂	1	1	yes	maximal, characteristic, complemented
9	#19133018	C₂	1	2	yes	maximal, complemented
10	C₈×#10621872	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×D₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×D₈×D₄₃	C₄	1	1	yes	characteristic
13	C₂²×#10621872	—	2	2	no	—
14	C₄×D₄×D₄₃	C₂²	1	2	yes	—
15	C₄×D₃₄₄	C₂²	1	1	yes	characteristic
16	D₈×Dic₄₃	C₄	1	1	yes	characteristic
17	#14582981	C₄	1	1	yes	characteristic
18	C₄×#10621882	C₂²	1	2	yes	—
19	#14582979	C₄	1	2	yes	—
20	#14582978	C₂²	1	2	yes	complemented
21	#14582976	C₂²	1	2	yes	complemented
22	#14582970	—	2	2	no	—
23	#14582967	—	2	2	no	—
24	D₄×C₄₃⋊C₈	C₂²	1	2	yes	complemented
25	#14582950	C₂²	1	1	yes	characteristic
26	#107×D₄₃	C₄	1	1	yes	characteristic
27	#14582921	C₂²	1	2	yes	—
28	#102×D₄₃	C₄	1	2	yes	—
29	#14582861	—	2	2	no	—
30	C₄×#10621872	C₂²	1	1	yes	characteristic
31	C₄×C₈×D₄₃	C₂²	1	1	yes	characteristic
32	#14582652	C₂²	1	1	yes	characteristic, complemented
33	#14582651	C₂²	1	2	yes	complemented
34	#14582628	C₂²	1	2	yes	complemented
35	D₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	complemented
36	#14582626	C₂²	1	2	yes	complemented
37	#14582621	C₂²	1	1	yes	characteristic, complemented
38	#14582620	C₂²	1	1	yes	characteristic, complemented
39	C₈×C₄₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
40	C₄×D₈×C₄₃	C₂²	1	1	yes	characteristic
41	C₈×D₄×C₄₃	C₂²	1	2	yes	complemented
42	C₄₃×#335	C₂²	1	1	yes	characteristic, complemented
43	C₄₃×D₄⋊C₈	C₂²	1	2	yes	complemented
44	C₈²×C₄₃	C₂²	1	1	yes	characteristic, complemented
45	C₂×D₄×D₄₃	C₂×C₄	1	2	yes	—
46	C₂²×C₄×D₄₃	—	2	2	no	—
47	C₂×D₃₄₄	C₂×C₄	1	1	yes	characteristic
48	C₂×#10621882	C₂×C₄	1	2	yes	—
49	D₈×D₄₃	—	2	4	no	—
50	C₂×#10621872	—	2	2	no	—
51	C₂×#10621872	—	2	2	no	—
52	C₂×#10621872	—	2	2	no	—
53	C₂×#10621872	—	4	8	no	—
54	C₂×#10621872	D₄	1	1	yes	characteristic
55	C₂×#10621872	D₄	1	1	yes	characteristic
56	C₂²×C₄₃⋊C₈	—	2	2	no	—
57	C₂×C₈×D₄₃	C₂×C₄	1	1	yes	characteristic
58	C₂×C₈×D₄₃	C₂×C₄	1	1	yes	characteristic
59	C₄×D₁₇₂	C₂³	1	2	yes	—
60	D₄×Dic₄₃	C₂×C₄	1	2	yes	—
61	#13063287	C₂×C₄	1	2	yes	—
62	C₄×C₂²⋊D₄₃	—	2	2	no	—
63	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
64	C₄⋊C₄×D₄₃	C₂×C₄	1	2	yes	—
65	C₂²⋊C₄×D₄₃	—	2	2	no	—
66	C₄²×D₄₃	C₂³	1	1	yes	characteristic
67	#13063259	C₂×C₄	1	1	yes	characteristic
68	#13063258	C₂×C₄	1	2	yes	—
69	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
70	Dic₄₃⋊C₈	—	2	2	no	—
71	Dic₄₃⋊C₈	—	2	1	no	—
72	#13063247	C₂×C₄	1	2	yes	—
73	#13063246	C₂×C₄	1	2	yes	—
74	#13063245	C₂×C₄	1	2	yes	—
75	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
76	(C₂×D₄₃)⋊C₈	—	2	1	no	—
77	(C₂×D₄₃)⋊C₈	—	2	2	no	—
78	(C₂×D₄₃)⋊C₈	—	2	2	no	—
79	#13063235	D₄	1	1	yes	characteristic
80	#13063235	D₄	1	1	yes	characteristic
81	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
82	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
83	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
84	C₈×Dic₄₃	C₂×C₄	1	1	yes	characteristic
85	C₈×Dic₄₃	C₂×C₄	1	1	yes	characteristic
86	C₂×D₈×C₄₃	C₂×C₄	1	1	yes	characteristic
87	C₂²×C₈×C₄₃	—	2	2	no	—
88	C₄×D₄×C₄₃	C₂³	1	2	yes	—
89	#107×C₄₃	C₂×C₄	1	1	yes	characteristic
90	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
91	#102×C₄₃	C₂×C₄	1	2	yes	—
92	C₂²⋊C₈×C₄₃	—	2	2	no	—
93	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
94	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
95	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
96	C₂³×D₄₃	—	2	2	no	—
97	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₄₃	—	2	2	no	—
99	C₂×C₂²⋊D₄₃	—	2	2	no	—
100	C₂²×Dic₄₃	—	2	2	no	—
101	D₄×D₄₃	—	2	4	no	—
102	D₄×D₄₃	—	4	2	no	—
103	C₂×D₁₇₂	C₂²×C₄	1	2	yes	—
104	C₂×C₄×D₄₃	—	2	2	no	—
105	C₂×C₄×D₄₃	—	2	2	no	—
106	C₂×C₄×D₄₃	—	2	2	no	—
107	C₂×C₄×D₄₃	—	4	4	no	—
108	C₂×C₄×D₄₃	—	4	4	no	—
109	C₂×C₄×D₄₃	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
111	C₂×C₄×D₄₃	#41	1	1	yes	characteristic
112	D₈×C₄₃	M₁₆	1	4	yes	complemented
113	C₂×C₈×C₄₃	—	2	2	no	—
114	C₂×C₈×C₄₃	—	2	1	no	—
115	C₂×C₈×C₄₃	—	4	4	no	—
116	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
119	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
120	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
121	C₂²⋊C₄×C₄₃	—	2	2	no	—
122	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
123	C₂²⋊Dic₄₃	—	2	2	no	—
124	#10621882	—	2	4	no	—
125	(C₂×D₄₃)⋊C₄	—	2	2	no	—
126	(C₂×D₄₃)⋊C₄	—	2	2	no	—
127	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
128	Dic₄₃⋊C₄	—	2	2	no	—
129	C₄×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
130	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
131	C₄×Dic₄₃	#41	1	1	yes	characteristic
132	C₂×C₄₃⋊C₈	—	2	2	no	—
133	C₂×C₄₃⋊C₈	—	2	1	no	—
134	C₂×C₄₃⋊C₈	—	4	4	no	—
135	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
138	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
139	D₃₄₄	—	2	2	no	—
140	#10621872	—	2	2	no	—
141	#10621872	—	4	4	no	—
142	#10621872	—	4	4	no	—
143	#10621872	—	4	4	no	—
144	#10621872	D₈	1	4	yes	direct product factor
145	C₈×D₄₃	—	2	2	no	—
146	C₈×D₄₃	—	4	1	no	—
147	C₂³×C₄₃	—	2	2	no	—
148	C₂²×D₄₃	—	2	2	no	—
149	C₂²×D₄₃	—	4	4	no	—
150	C₂²×D₄₃	—	4	4	no	—
151	C₂²×D₄₃	—	8	2	no	—
152	C₂²×D₄₃	C₄×D₄	1	1	yes	characteristic
153	D₄×C₄₃	—	2	2	no	—
154	D₄×C₄₃	C₂×M₁₆	1	4	yes	complemented
155	C₂×C₄×C₄₃	—	2	2	no	—
156	C₂×C₄×C₄₃	—	4	2	no	—
157	C₂×C₄×C₄₃	—	4	2	no	—
158	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
159	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
161	C₂²⋊D₄₃	—	4	4	no	—
162	C₂×Dic₄₃	—	2	2	no	—
163	C₂×Dic₄₃	—	4	4	no	—
164	C₂×Dic₄₃	C₄×D₄	1	1	yes	characteristic
165	C₂×Dic₄₃	C₄×D₄	1	1	yes	characteristic
166	C₂×Dic₄₃	C₄×D₄	1	1	yes	characteristic
167	D₁₇₂	—	2	2	no	—
168	D₁₇₂	—	2	2	no	—
169	C₄×D₄₃	—	2	1	no	—
170	C₄×D₄₃	—	2	1	no	—
171	C₄×D₄₃	—	4	1	no	—
172	C₄×D₄₃	—	4	4	no	—
173	C₄×D₄₃	—	4	2	no	—
174	C₄×D₄₃	—	4	2	no	—
175	C₄×D₄₃	—	4	4	no	—
176	C₄×D₄₃	C₂×D₈	1	2	yes	—
177	C₄×D₄₃	#135	1	2	yes	—
178	C₈×C₄₃	—	2	1	no	—
179	C₈×C₄₃	—	2	1	no	—
180	C₈×C₄₃	—	4	1	no	—
181	C₈×C₄₃	—	4	2	no	—
182	C₈×C₄₃	C₂×M₁₆	1	2	yes	complemented
183	C₈×C₄₃	C₂×D₈	1	2	yes	complemented
184	C₄₃⋊C₈	—	2	1	no	—
185	C₄₃⋊C₈	—	2	1	no	—
186	C₄₃⋊C₈	—	2	1	no	—
187	C₄₃⋊C₈	—	4	1	no	—
188	C₄₃⋊C₈	—	4	2	no	—
189	C₄₃⋊C₈	C₂×D₈	1	2	yes	complemented
190	M₁₆×D₈	—	43	1	no	maximal, Sylow
191	C₂²×C₄₃	—	2	4	no	—
192	C₂²×C₄₃	—	4	2	no	—
193	C₂²×C₄₃	—	4	2	no	—
194	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
195	C₂×D₄₃	—	2	1	no	—
196	C₂×D₄₃	—	2	1	no	—
197	C₂×D₄₃	—	4	2	no	—
198	C₂×D₄₃	—	4	2	no	—
199	C₂×D₄₃	—	4	2	no	—
200	C₂×D₄₃	—	8	8	no	—
201	C₂×D₄₃	C₄×D₈	1	2	yes	—
202	C₄×C₄₃	—	2	1	no	—
203	C₄×C₄₃	—	4	2	no	—
204	C₄×C₄₃	C₂²×M₁₆	1	1	yes	characteristic
205	C₄×C₄₃	#568	1	1	yes	characteristic
206	C₄×C₄₃	C₂²×D₈	1	1	yes	characteristic
207	C₄×C₄₃	C₂×#135	1	1	yes	characteristic
208	Dic₄₃	—	2	1	no	—
209	Dic₄₃	—	2	1	no	—
210	Dic₄₃	—	4	2	no	—
211	Dic₄₃	C₄×D₈	1	2	yes	—
212	C₂×C₄×D₈	—	43	1	no	—
213	D₄×M₁₆	—	43	2	no	—
214	#1589	—	43	1	no	—
215	#1589	—	43	1	no	—
216	#1581	—	43	2	no	—
217	#1581	—	43	2	no	—
218	C₈×D₈	—	43	1	no	—
219	C₈×D₈	D₄₃	1	1	yes	characteristic, complemented
220	#1567	—	43	1	no	—
221	#1486	—	43	2	no	—
222	C₈×M₁₆	—	43	1	no	—
223	C₂×C₄₃	—	4	4	no	—
224	C₂×C₄₃	D₄×M₁₆	1	1	yes	characteristic
225	C₂×C₄₃	C₂×C₄×D₈	1	1	yes	characteristic
226	C₂×C₄₃	#2957	1	1	yes	characteristic
227	D₄₃	—	2	2	no	—
228	D₄₃	—	8	2	no	—
229	C₂²×D₈	—	43	1	no	—
230	C₂²×M₁₆	—	86	2	no	—
231	C₂×C₄×D₄	—	43	2	no	—
232	C₄×D₈	—	43	1	no	—
233	C₄×D₈	—	43	2	no	—
234	C₄×D₈	—	43	1	no	—
235	C₄×D₈	—	43	2	no	—
236	C₄×D₈	—	43	1	no	—
237	C₄×D₈	C₂×D₄₃	1	1	yes	characteristic
238	#436	—	43	2	no	—
239	#436	—	43	2	no	—
240	#435	—	86	2	no	—
241	#435	—	86	2	no	—
242	C₈×D₄	—	43	2	no	—
243	C₈×D₄	C₂×D₄₃	1	2	yes	complemented
244	#431	—	43	1	no	—
245	C₂×#107	—	43	1	no	—
246	#423	—	43	2	no	—
247	C₂×#102	—	43	2	no	—
248	#407	—	86	2	no	—
249	C₄×M₁₆	—	43	1	no	—
250	C₂×C₄×C₈	—	43	1	no	—
251	#335	—	43	2	no	—
252	#335	—	43	1	no	—
253	#335	C₂×D₄₃	1	1	yes	characteristic, complemented
254	D₄⋊C₈	—	43	2	no	—
255	D₄⋊C₈	—	43	2	no	—
256	D₄⋊C₈	—	43	2	no	—
257	D₄⋊C₈	C₂×D₄₃	1	2	yes	complemented
258	#322	—	43	1	no	—
259	#322	—	43	1	no	—
260	C₈²	—	43	1	no	—
261	C₈²	C₂×D₄₃	1	1	yes	characteristic, complemented
262	C₄₃	M₁₆×D₈	1	1	yes	characteristic, complemented, Sylow
263	C₂²×D₄	—	43	2	no	—
264	C₂³×C₄	—	86	2	no	—
265	C₂×D₈	—	43	2	no	—
266	C₂×D₈	—	43	1	no	—
267	C₂×D₈	—	86	4	no	—
268	C₂×D₈	C₄×D₄₃	1	1	yes	characteristic
269	C₂×M₁₆	—	43	1	no	—
270	C₂×M₁₆	—	43	1	no	—
271	C₂×M₁₆	—	86	2	no	—
272	C₂×M₁₆	—	86	2	no	—
273	C₂×M₁₆	—	86	2	no	—
274	C₂×M₁₆	—	172	8	no	—
275	C₂²×C₈	—	2	2	no	—
276	C₂²×C₈	—	43	1	no	—
277	C₂²×C₈	—	43	1	no	—
278	C₂²×C₈	—	86	2	no	—
279	C₄×D₄	—	43	2	no	—
280	C₄×D₄	—	43	2	no	—
281	C₄×D₄	—	43	2	no	—
282	C₄×D₄	—	86	2	no	—
283	C₄×D₄	—	86	2	no	—
284	C₄×D₄	C₂²×D₄₃	1	2	yes	—
285	C₂×C₄⋊C₄	—	43	2	no	—
286	C₂×C₂²⋊C₄	—	86	2	no	—
287	C₂×C₄²	—	43	1	no	—
288	#107	—	43	1	no	—
289	#107	—	43	2	no	—
290	#107	C₄×D₄₃	1	1	yes	characteristic
291	C₄⋊C₈	—	43	2	no	—
292	C₄⋊C₈	—	86	2	no	—
293	C₄⋊C₈	—	86	1	no	—
294	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
295	#102	—	43	2	no	—
296	#102	—	43	2	no	—
297	#102	—	43	2	no	—
298	#102	C₄×D₄₃	1	2	yes	—
299	C₂²⋊C₈	—	2	2	no	—
300	C₂²⋊C₈	—	86	2	no	—
301	C₂²⋊C₈	—	86	1	no	—
302	C₂²⋊C₈	—	86	2	no	—
303	C₂²⋊C₈	—	86	2	no	—
304	#97	—	43	1	no	—
305	#97	—	43	1	no	—
306	C₄×C₈	—	43	1	no	—
307	C₄×C₈	—	43	1	no	—
308	C₄×C₈	—	43	1	no	—
309	C₄×C₈	—	43	1	no	—
310	C₄×C₈	—	43	1	no	—
311	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
312	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
313	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
314	C₂⁴	—	86	2	no	—
315	C₂×D₄	—	43	2	no	—
316	C₂×D₄	—	86	2	no	—
317	C₂×D₄	—	86	4	no	—
318	C₂×D₄	—	172	2	no	—
319	C₂×D₄	C₂×C₄×D₄₃	1	2	yes	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	43	1	no	—
322	C₂²×C₄	—	43	1	no	—
323	C₂²×C₄	—	43	1	no	—
324	C₂²×C₄	—	86	2	no	—
325	C₂²×C₄	—	86	2	no	—
326	C₂²×C₄	—	86	2	no	—
327	C₂²×C₄	—	86	2	no	—
328	C₂²×C₄	—	172	4	no	—
329	C₂²×C₄	—	172	4	no	—
330	D₈	—	86	4	no	—
331	D₈	—	86	2	no	—
332	D₈	#10621872	1	4	yes	direct product factor
333	M₁₆	—	43	4	no	—
334	M₁₆	—	86	2	no	—
335	M₁₆	—	172	4	no	—
336	M₁₆	—	172	4	no	—
337	M₁₆	—	172	4	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	4	4	no	—
341	C₂×C₈	—	43	1	no	—
342	C₂×C₈	—	43	1	no	—
343	C₂×C₈	—	43	1	no	—
344	C₂×C₈	—	43	1	no	—
345	C₂×C₈	—	86	2	no	—
346	C₂×C₈	—	86	2	no	—
347	C₂×C₈	—	86	1	no	—
348	C₂×C₈	—	172	1	no	—
349	C₂×C₈	—	172	4	no	—
350	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
351	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
352	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
353	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
354	C₄⋊C₄	—	43	2	no	—
355	C₄⋊C₄	—	86	2	no	—
356	C₄⋊C₄	C₂×C₄×D₄₃	1	2	yes	—
357	C₂²⋊C₄	—	2	2	no	—
358	C₂²⋊C₄	—	86	2	no	—
359	C₂²⋊C₄	—	86	2	no	—
360	C₂²⋊C₄	—	86	2	no	—
361	C₄²	—	43	1	no	—
362	C₄²	—	43	1	no	—
363	C₄²	—	43	1	no	—
364	C₄²	C₂³×D₄₃	1	1	yes	characteristic
365	C₂³	—	2	2	no	—
366	C₂³	—	43	1	no	—
367	C₂³	—	86	2	no	—
368	C₂³	—	344	2	no	—
369	C₂³	—	172	4	no	—
370	C₂³	—	172	4	no	—
371	D₄	—	2	2	no	—
372	D₄	—	86	2	no	—
373	D₄	—	86	2	no	—
374	D₄	—	172	4	no	—
375	D₄	C₂×#10621872	1	4	yes	complemented
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	43	1	no	—
380	C₂×C₄	—	43	2	no	—
381	C₂×C₄	—	43	2	no	—
382	C₂×C₄	—	43	1	no	—
383	C₂×C₄	—	43	1	no	—
384	C₂×C₄	—	86	1	no	—
385	C₂×C₄	—	86	1	no	—
386	C₂×C₄	—	86	2	no	—
387	C₂×C₄	—	172	1	no	—
388	C₂×C₄	—	172	4	no	—
389	C₂×C₄	—	172	4	no	—
390	C₂×C₄	—	172	4	no	—
391	C₂×C₄	—	172	2	no	—
392	C₂×C₄	—	172	2	no	—
393	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
394	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
395	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
396	C₈	—	2	1	no	—
397	C₈	—	2	1	no	—
398	C₈	—	4	1	no	—
399	C₈	—	4	2	no	—
400	C₈	—	43	2	no	—
401	C₈	—	86	1	no	—
402	C₈	—	86	1	no	—
403	C₈	—	86	1	no	—
404	C₈	—	172	1	no	—
405	C₈	—	172	2	no	—
406	C₈	C₂×#10621872	1	2	yes	complemented
407	C₈	D₈×D₄₃	1	2	yes	complemented
408	C₂²	—	2	4	no	—
409	C₂²	—	4	2	no	—
410	C₂²	—	4	2	no	—
411	C₂²	—	43	2	no	—
412	C₂²	—	86	1	no	—
413	C₂²	—	86	1	no	—
414	C₂²	—	344	8	no	—
415	C₂²	—	172	2	no	—
416	C₂²	—	172	2	no	—
417	C₂²	—	172	2	no	—
418	C₂²	C₄×D₄×D₄₃	1	1	yes	characteristic
419	C₄	—	2	1	no	—
420	C₄	—	4	2	no	—
421	C₄	—	43	2	no	—
422	C₄	—	86	1	no	—
423	C₄	—	86	1	no	—
424	C₄	—	172	2	no	—
425	C₄	C₂²×#10621872	1	1	yes	characteristic
426	C₄	#14583664	1	1	yes	characteristic
427	C₄	C₂×D₈×D₄₃	1	1	yes	characteristic
428	C₄	#135×D₄₃	1	1	yes	characteristic
429	C₂	—	4	4	no	—
430	C₂	—	86	2	no	—
431	C₂	—	344	2	no	—
432	C₂	D₄×#10621872	1	1	yes	characteristic
433	C₂	C₄×D₈×D₄₃	1	1	yes	characteristic
434	C₂	#19143507	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₄²	C₂³×D₄₃
Fitting	C₈×D₈×C₄₃	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	C₂×D₈×D₄₃	C₄
cosocle	C₄²×C₄₃	C₂⁴
hypercenter	C₈×D₈	D₄₃
hypocenter	C₄₃	M₁₆×D₈
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₈×D₈

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. D₄×#10621872	C₂	semidirect
3. #19133481	C₂	semidirect
4. #19133479	C₂	semidirect
5. #19133424	C₂	semidirect
6. #19133421	C₂	semidirect
7. D₈×C₄₃⋊C₈	C₂	semidirect
8. #19133352	C₂	semidirect
9. #19133018	C₂	semidirect
10. C₈×#10621872	C₂	semidirect
11. C₈×D₈×C₄₃	C₂	semidirect
20. #14582978	C₂²	semidirect
21. #14582976	C₂²	semidirect
24. D₄×C₄₃⋊C₈	C₂²	semidirect
32. #14582652	C₂²	semidirect
33. #14582651	C₂²	semidirect
34. #14582628	C₂²	semidirect
35. D₄⋊(C₄₃⋊C₈)	C₂²	semidirect
36. #14582626	C₂²	semidirect
37. #14582621	C₂²	semidirect
38. #14582620	C₂²	semidirect
39. C₈×C₄₃⋊C₈	C₂²	semidirect
41. C₈×D₄×C₄₃	C₂²	semidirect
42. C₄₃×#335	C₂²	semidirect
43. C₄₃×D₄⋊C₈	C₂²	semidirect
44. C₈²×C₄₃	C₂²	semidirect
112. D₈×C₄₃	M₁₆	semidirect
144. #10621872	D₈	direct (N × H)
154. D₄×C₄₃	C₂×M₁₆	semidirect
182. C₈×C₄₃	C₂×M₁₆	semidirect
183. C₈×C₄₃	C₂×D₈	semidirect
189. C₄₃⋊C₈	C₂×D₈	semidirect
219. C₈×D₈	D₄₃	semidirect
243. C₈×D₄	C₂×D₄₃	semidirect
253. #335	C₂×D₄₃	semidirect
257. D₄⋊C₈	C₂×D₄₃	semidirect
261. C₈²	C₂×D₄₃	semidirect
262. C₄₃	M₁₆×D₈	semidirect
332. D₈	#10621872	direct (N × H)
375. D₄	C₂×#10621872	semidirect
406. C₈	C₂×#10621872	semidirect
407. C₈	D₈×D₄₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄×D₈×D₄₃	2
D₄×#10621872	2
#19133481	2
#19133479	2
#19133424	2
#19133421	2
D₈×C₄₃⋊C₈	2
#19133352	2
#19133018	2
C₈×#10621872	2
C₈×D₈×C₄₃	2
M₁₆×D₈	43

Subgroups — D8×#10621872 #25068014

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₈×#10621872 #25068014